Question

The local sporting goods store is advertising a 20% off sale on a new ski coat. If the saleprice is $199, what was the original price of the ski coat?Use X in the equation

Answer 1

Let us call the original price x, shall we?

We are told that after the 20% off on x, the price is $199. Therefore, we can write this situation as

`x-(20)/(100)x=199`

Simplifying this gives

`(80)/(100)x=199\text{.}`

Alternatively, we could say that after 20% of on x, the sale price is now 80% of the original price. In which case, we have the equation

`(80)/(100)x=199.`

which is the same equation as we got first.

Now we need to solve for x. We do this by multiplying both sides by 100 and then dividing by 80:

`100*(80)/(100)x=199*100`
`\Rightarrow80x=19900`

and dividing by 80:

`(80x)/(80)=(19900)/(80)`
`\Rightarrow x=248.75`

Hence, the original price is $248.75.